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Publisher: Cambridge University Press   (Total: 374 journals)

 Compositio MathematicaJournal Prestige (SJR): 3.139 Citation Impact (citeScore): 1Number of Followers: 1      Subscription journal ISSN (Print) 0010-437X - ISSN (Online) 1570-5846 Published by Cambridge University Press  [374 journals]
• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++-Kähler+structures&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2019&rft.volume=155&rft.spage=455&rft.epage=483&rft.aulast=Rao&rft.aufirst=Sheng&rft.au=Sheng+Rao&rft.au=Xueyuan+Wan,+Quanting+Zhao&rft_id=info:doi/10.1112/S0010437X19007085">On local stabilities of $p$ -Kähler structures
• Authors: Sheng Rao; Xueyuan Wan, Quanting Zhao
Pages: 455 - 483
Abstract: By use of a natural extension map and a power series method, we obtain a local stability theorem for $p$ -Kähler structures with the $(p,p+1)$ th mild $\unicode[STIX]{x2202}\overline{\unicode[STIX]{x2202}}$ -lemma under small differentiable deformations.
PubDate: 2019-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007085
Issue No: Vol. 155, No. 3 (2019)

• Spinor groups with good reduction
• Authors: Vladimir I. Chernousov; Andrei S. Rapinchuk, Igor A. Rapinchuk
Pages: 484 - 527
Abstract: Let $K$ be a two-dimensional global field of characteristic $\neq 2$ and let $V$ be a divisorial set of places of $K$ . We show that for a given $n\geqslant 5$ , the set of $K$ -isomorphism classes of spinor groups $G=\operatorname{Spin}_{n}(q)$ of nondegenerate $n$ -dimensional quadratic forms over $K$ that have good reduction at all $v\in V$ is finite. This result yields some other finiteness properties, such as the finiteness of the genus $\mathbf{gen}_{K}(G)$ and the properness of the global-to-local map in Galois cohomology. The proof relies on the finiteness of the unramified cohomology groups
PubDate: 2019-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X1900705X
Issue No: Vol. 155, No. 3 (2019)

• The inertia operator on the motivic Hall algebra
• Authors: Kai Behrend; Pooya Ronagh
Pages: 528 - 598
Abstract: We study the action of the inertia operator on the motivic Hall algebra and prove that it is diagonalizable. This leads to a filtration of the Hall algebra, whose associated graded algebra is commutative. In particular, the degree 1 subspace forms a Lie algebra, which we call the Lie algebra of virtually indecomposable elements, following Joyce. We prove that the integral of virtually indecomposable elements admits an Euler characteristic specialization. In order to take advantage of the fact that our inertia groups are unit groups in algebras, we introduce the notion of algebroid.
PubDate: 2019-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007881
Issue No: Vol. 155, No. 3 (2019)

• Topological Fukaya category and mirror symmetry for punctured surfaces
• Authors: James Pascaleff; Nicolò Sibilla
Pages: 599 - 644
Abstract: In this paper we establish a version of homological mirror symmetry for punctured Riemann surfaces. Following a proposal of Kontsevich we model A-branes on a punctured surface $\unicode[STIX]{x1D6F4}$ via the topological Fukaya category. We prove that the topological Fukaya category of $\unicode[STIX]{x1D6F4}$ is equivalent to the category of matrix factorizations of a certain mirror LG model $(X,W)$ . Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which are of independent interest.
PubDate: 2019-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007073
Issue No: Vol. 155, No. 3 (2019)

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